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New General

Mathematics

FOR SENIOR SECONDARY SCHOOLS

TEACHER'S GUIDE

H. Otto

9781292119748_ngm_mat_fm1_tg_eng_ng.indb 1

Pearson Education Limited

Edinburgh Gate

Harlow

Essex CM20 2JE

England

and Associated Companies throughout the world

© Pearson PLC

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or

transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,

without the prior permission of the publishers.

First published in 2015

ISBN 9781292119748

Cover design by Mark Standley

Typesetting by

Author: Helena Otto

Acknowledgements

The Publisher would like to thank the following for the use of copyrighted images in this publication:

Cover image: Science Photo Library Ltd; Shutterstock.com It is illegal to photocopy any page of this book without the written perm ission of the copyright holder. Every effort has been made to trace the copyright holders. In the event of unintentional omissions or errors, any information that would enable the publisher to make the proper arrangements will be appreciated.

9781292119748_ngm_mat_fm1_tg_eng_ng.indb 2

Review of Junior Secondary School course iv

Chapter 1:

Numerical processes 1: Indices and logarithms 1

Chapter 2:

Geometry 1: Formal geometry: Triangles and polygons 5

Chapter 3:

Numerical processes 2: Fractions, decimals, percentages and number bases 13

Chapter 4:

Algebraic processes 1: Simplification and substitution 15

Chapter 5:

Sets 1 18

Chapter 6:

Algebraic processes 2: Equations and formulae 21

Chapter 7:

Algebraic processes 3: Linear and quadratic graphs 25

Chapter 8:

Sets 2: Practical applications 28

Chapter 9:

Logical reasoning: Simple and compound statements 29

Chapter 10:

Algebraic processes 4: Quadratic equations 30

Chapter 11: Trigonometry 1: Solving right-angled triangles 34

Chapter 12:

Mensuration 1: Plane shapes 37

Chapter 13:

Numerical processes 3: Ratio, rate and proportion 39

Chapter 14:

Statistics: Data presentation 41

Chapter 15:

Mensuration 2: Solid shapes 43

Chapter 16:

Geometry 2: Constructions and loci 45

Chapter 17:

Trigonometry 2: Angles between 0° and 360° 47

Chapter 18:

Algebraic processes 5: Variation 50

Chapter 19:

Numerical processes 4: Tax and monetary exchange 51

Chapter 20:

Numerical processes 5: Modular arithmetic 52

9781292119748_ngm_mat_fm1_tg_eng_ng.indb 3

Review of Junior Secondary School course

1. Number and numeration

2. Algebraic processes

4. Geometry and mensuration

5. Statistics and probability

2. Teaching and learning materials

Teachers should have the Mathematics textbook of

the Junior Secondary School Course and Book 1 of the Senior Secondary School Course.

Students should have:

1. Book 1

2. An Exercise book

3. Graph paper

4. A scientific calculator, if possible.

3. Glossary of terms

Algebraic expression A mathematical phrase that

can contains ordinary numbers, variables (such as x or y ) and operators (such as add, subtract, multiply, and divide). For example, 3 x 2 y - 3y 2 + 4.

Algebraic sentence is another word for an

algebraic equation where two algebraic expressions are equal to each other.

Angle A measure of rotation or turning and we use

a protractor to measure the size of an angle.

Angle of depression The angle through which the

eyes must look downward from the horizontal to see a point below.

Angle of elevation The angle through which the

eyes must look upward from the horizontal to see a point above.

Bimodal means that the data has two modes.

Cartesian plane A coordinate system that

specifies each point in a plane uniquely by a pair of numerical coordinates, which are the perpendicular distances of the point from two fixed perpendicular directed lines or axes, measured in the same unit of length. The word

Cartesian comes from the inventor of this plane

namely René Descartes, a French mathematician.

Coefficient

a numerical or constant or quantity 0 placed before and multiplying the variable in an algebraic expression (for example, 4 in 4 x y

Common fraction (also called a vulgar fraction

or simple fraction) Any number written as a _ b where a and b are both whole numbers and where a b

Coordinates of point A, for example, (1, 2)

gives its position on a Cartesian plane. The first coordinate ( x -coordinate) always gives the distance along the x -axis and the second coordinate ( y -coordinate) gives the distance along the y -axis. Data Distinct pieces of information that can exist in a variety of forms, such as numbers. Strictly speaking, data is the plural of datum , a single piece of information. In practice, however, people use data as both the singular and plural form of the word.

Decimal place values A positional system of

notation in which the position of a number with respect to the decimal point determines its value. In the decimal (base 10) system, the value of each digit is based on the number 10. Each position in a decimal number has a value that is a power of 10.

Denominator The part of the fraction that is

written below the line. The 4 in 3 _ 4 , for example, is the denominator of the fraction. It also tells you what kind of fraction it is. In this case, the kind of fraction is quarters.

Directed numbers Positive and negative numbers

are called directed numbers and are shown on a number line. These numbers have a certain direction with respect to zero. If a number is positive, it is on the right-hand side of 0 on the number line. If a number is negative, it is on the left-hand side of the 0 on the number line.

Direct proportion The relationship between

quantities of which the ratio remains constant. If a and b are directly proportional, then a _ b = a constant value (for example, k).

Direct variation Two quantities a and b vary

directly if, when a changes, then b changes in the same ratio. That means that: If a doubles in value, b will also double in value. If a increases by a factor of 3, then b will also increase by a factor of 3.

Edge A line segment that joins two vertices of a

solid.

9781292119748_ngm_mat_fm1_tg_eng_ng.indb 4

Review of Junior Secondary School course

is the process of solving a system of simultaneous equations by using various techniques to successively remove the variables.

Equivalent fractions Fractions that are multiples

of each other, for example, 3 _ 4

3 × 2

____

4 × 2

3 × 3

____

4 × 3

and so on.

Expansion of an algebraic expression means that

brackets are removed by multiplication Faces of a solid A flat (planar) surface that forms part of the boundary of the solid object; a three- dimensional solid bounded exclusively by flat faces is a polyhedron.

Factorisation of an algebraic expression means

that we write an algebraic expression as the product of its factors.

Graphical method used to solve simultaneous

linear equations means that the graphs of the equations are drawn. The solution is where the two graphs intersect (cut) each other.

Highest Common Factor (HCF) of a set of

numbers is the highest factor that all those numbers have in common or the highest number that can divide into all the numbers in the set.

The HCF of 18, 24 and 30, for example, is 6.

Inverse proportion The relationship between two

variables in which their product is a constant.

When one variable increases, the other decreases

in proportion so that the product is unchanged. If b is inversely proportional to a , the equation is in the form b k _ a (where k is a constant).

Inverse variation: Two quantities a and b vary

inversely if, when a changes, then b changes by the same ratio inversely. That means that:

If a doubles, then b halves in value.

If a increases by a factor of 3, then b decreases by a factor of 1 _ 3

Joint variation of three quantities x, y and z

means that x and y are directly proportional, for example, and xquotesdbs_dbs4.pdfusesText_7

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